自适应多重检验的一致性
On the consistency of adaptive multiple tests
摘要：
当同时测试$m$假设时，已经做了很多努力来控制“错误发现率”（FDR）。FDR是“错误发现比例”$\text{FDP}=V/R$的期望值，由错误拒绝数$V$和所有拒绝数$R$的比率给出。在本文中，我们有一个更密切的关注FDP自适应线性逐步上升多次测试。这些检验通过估计真实零假设的未知量$m_0$来扩展众所周知的Benjamini和Hochberg检验。我们给出精确的有限样本公式的高阶矩的FDP，特别是，其方差。使用这些使我们能够精确地讨论自适应升压测试的一致性。我们提出了充分和必要条件的一致性估计$\widehat m_0$和潜在的概率制度。我们将我们的结果适用于各种调整参数和（可能）数据驱动的权重的广义Storey型估计的凸组合。相应的升压测试允许灵活调整。此外，这些测试控制有限样本量的FDR。我们比较了这些测试与经典的Benjamini和Hochberg测试，并讨论了它的优点。
英文摘要：
Much effort has been done to control the "false discovery rate" (FDR) when $m$ hypotheses are tested simultaneously. The FDR is the expectation of the "false discovery proportion" $\text{FDP}=V/R$ given by the ratio of the number of false rejections $V$ and all rejections $R$. In this paper, we have a closer look at the FDP for adaptive linear step-up multiple tests. These tests extend the well known Benjamini and Hochberg test by estimating the unknown amount $m_0$ of the true null hypotheses. We give exact finite sample formulas for higher moments of the FDP and, in particular, for its variance. Using these allows us a precise discussion about the consistency of adaptive step-up tests. We present sufficient and necessary conditions for consistency on the estimators $\widehat m_0$ and the underlying probability regime. We apply our results to convex combinations of generalized Storey type estimators with various tuning parameters and (possibly) data-driven weights. The corresponding step-up tests allow a flexible adaptation. Moreover, these tests control the FDR at finite sample size. We compare these tests to the classical Benjamini and Hochberg test and discuss the advantages of it.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
